Date: 2024-12-13

Time: 15:30-16:30 (Montreal time)

Location: In person, Burnside 1104

https://mcgill.zoom.us/j/81501161882

Meeting ID: 815 0116 1882

Passcode: None

Abstract:

The problem of testing that a random sample is drawn from a specific probability distribution is an old one, the most famous example perhaps being the problem of testing that a sequence of playing cards was drawn from a fairly shuffled deck. In recent years, random data consisting of positive definite (symmetric) matrices have appeared in areas of applied research such as factor analysis, diffusion tensor imaging, wireless communication systems, synthetic aperture radar, and models of financial volatility. Given a random sample of positive definite matrices, we develop a goodness-of-fit test for the Wishart distributions. We derive the asymptotic distribution of the test statistic in terms of a certain Gaussian random field, and we obtain an explicit formula for the corresponding covariance operator. The eigenfunctions of the covariance operator are determined explicitly, and the eigenvalues are shown to satisfy certain interlacing properties. As an application, we carry out a test that a financial data set has a Wishart distribution and, finally, we describe some recent research and open problems on related goodness-of-fit tests.

Speaker

Donald Richards is a Distinguished Professor Emeritus of Statistics at Penn State University. He received his Ph.D. in 1978 from the University of the West Indies. Throughout his career, Professor Richards has received numerous honors, including being elected a Fellow of the Institute of Mathematical Statistics and a Fellow of the American Mathematical Society. His research interests include Probability Theory, Multivariate Statistical Analysis, Harmonic Analysis, Analytic Number Theory, and Probabilistic Models in Actuarial Science.